On one G.I.Arkhipov’s theorem
https://doi.org/10.22405/2226-8383-2025-26-5-280-286
Abstract
In this paper in the model situation the generalized solution of the Cauchy problem of
linearalized the Corteveg – de Vriz equation are investigated. The solution are represented as
the Vinogradov’s trigonometric series, that permits to reduce the deduction to the Vinigradov’s method of the H.Weyl’s trigonometric sums.
About the Authors
Lyudmila Gennadievna Arkhipova
Lomonosov Moscow State University
Russian Federation
Russian Federation
Vladimir Nikolaevich Chubarikov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Vinogradov, I. M. 1980, “Method of trigonometric sums in the number theory, 2nd edit.”, Moscow, Nauka, pp. 144.
2. Arkhipov, G. I., “Oskolkov, K. I. 1989, Special trigonometric series and their applications”, Math. Trans., 62,𝑁𝑜.2. pp. 145 – 155.
3. Oskolkov, K. I. 1989, “I.M.Vinogradov’s series and integrals and their applications”, Proc. MIAN., 190, pp. 186 – 221.
4. Oskolkov, K. I. 1991, “I.M.Vinogradov’s series in the Caushy problem for equations of Schr´odinger type”, Proc. MIAN., 200, pp. 265 – 288.
5. Karatsuba, A. A. 1983, “Basics of analytic number theory, 2nd edit”, Moscow, Nauka, pp. 240.
6. Chubarikov, V. N. 2015, “The elementary deduction of the estimate of the complete rational arithmetical sum from a polynomial”, Chebyshev Trans., V.16, № . 3(55), pp. 452 – 461.
7. Chubarikov, V. N. 2015, “The exponent of the convergence of the mean-value of complete rational arithmetical sums”, Chebyshev Trans., V.16, № . 4(56), pp. 303 – 318.
8. Chubarikov, V. N. 2016, “Arithmetical sums from values of a polynomial”, Dokl. RAS, V.466, № . 2, pp. 152 – 153.
9. Chubarikov, V. N. 2015, “Complete rational arithmetical sums”, Вull. Moscow. Univ. Ser.I, Math., mech., № . 1, pp. 60 – 61.
10. Gijasi, A. H., 2025, “Chubarikov, V. N. On Vinogradov’s series over prime numbers”, Chebyshev Trans., V.26, № . 3, pp. 81 – 95.
11. Arkhipov, G. I., Sadovnichii, V. A., Chubarikov, V. N. 2004, “Lectures on mathematical analysis: Text-book for higher educ. of Inst. 4th edit.”, M.: Drofa, P. 640.
Review
For citations:
Arkhipova L.G., Chubarikov V.N. On one G.I.Arkhipov’s theorem. Chebyshevskii Sbornik. 2025;26(5):280-286. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-5-280-286
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